Answer the questions below about the quadratic function.

f(x)= -2x^2 - 4x - 1

1.) Does the function have a minimum or maximum value?

2.) Where does the minimum or maximum value occur?

3.) What is the functions minimum or maximum value?

Thank you for the opportunity to help you with your question!

1.

The minimum/maximum point is the point whereby the slope of the equation is zero. To get the slope of the equation, we differentiate the equation.

therefore, derivative = f'(x) =-4x-4

differentiating the derivative again gives f''(x) =-4

Therefore the functin has a maximum value since the second derivative is negative.

2.

From the first derivative the value of f'(x) = 0: At maximum or minimum point the gradient/slope of the curve is always zero.

therefore 0=-4x-4

4x=4

x=1

The maximum value is at the point where x=1

substituting into the original function gives f(x) =-2(1)^2-4x-1 = -7

hence (1, -7)

3. The function's maximum value is -7 as calculated above.

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